Can't hide object which particles are based on, without losing particles
Select the large torus.

Blender 2.7x

Press the M key and change the layer it lives on.



Then in render layers Shift-Select the layer you chose to remove that layer from being render.



Blender 2.8x

Go to the Object Properties panel.

De-select Show in renders



To explain this, the properties you are changing ar only for the instance you selected, not any instances that are generated by the particle system.